The goal of the research project is to carry out an extensive investigation of several areas of statistical methodology for the design and analysis of biomedical studies, applicable to various areas of health research, especially cancer clinical trials and cancer epidemiology. The research falls into four main categories. (A). Design and analysis of group sequential clinical trials. Emphasis will be on designs which allow flexibility yet maintain scientific validity. Designs with unequal and unpredictable increments in information between analyses will be investigated. Endpoints to be monitored include normal and t-statistics with various boundary types including equivalence and designs with an inner "futility" boundary. The setup accommodates longitudinal, survival and multivariate outcome data. Another flexibility feature to be considered is the incorporation of adaptive treatment assignment into traditional group sequential designs. (b). Design and evaluation of dynamic diagnostic indices that be used as tools for monitoring prospectively for onset of disease using accumulating serial biomarker measurements. Two methods will be investigated; the first is based on a hierarchical Bayes models and Gibbs sampling to obtain estimates; the second uses a generalization of a hidden Markov model which can be viewed as a frequentist (empirical Bayes) analog. (c). In most medical and epidemiological applications, there are features in data sets that complicate inferential procedures and their interpretation. Such features include over-dispersion, unobserved heterogeneity, measurement error, random effects, confounding variables, etc. A general methodology will be developed whereby output from statistical analysis based on more straightforward models can be easily adjusted to take account of extra bias and variability caused by such factors. (d). Various topics that arise when there are survival, longitudinal or repeated events endpoints. These include smooth estimation of intensity functions, motivated by a study of recurrent skin cancer; and the tradeoff between aspects of power and compliance in a clinical trial with survival endpoint when participants may be randomly assigned to treatment in clusters, as proposed in the PRECISE trial.